Particle-Hole Symmetry Breaking in the Fractional Quantum Hall Effect in the Lowest Landau Level Using Realistic Hamiltonians

In the 1980's it was shown that quasi-two dimensional electron gases within a semiconductor system exhibit a quantum Hall effect where the Hall resistances are quantized by rational values of h/e2. In this work, we perform a theoretical investigation using exact diagonalization on the spherical geometry on incompressible states within the fractional quantum Hall effect with a Hamiltonian that includes realistic effects like Landau level mixing and sub-band mixing. We investigate particle-hole symmetry in the lowest Landau level under realistic conditions. This work includes an analysis of the Haldane pseudopotentials, energy eigenvalues and various wave function overlaps that may help pinpoint any particle-hole symmetry breaking. We conclude that particle-hole symmetry is broken, as determined by energy gaps, between states related via particle-hole conjugation. However, we find that particle-hole symmetry is largely maintained as determined by the effective mass of composite fermions. Finally, we comment and make connection to recent experimental observations regarding particle-hole symmetry in the lowest Landau level fractional quantum Hall effect